Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in JAVA):

Solution:
import java.util.Scanner;

/**
 *
 * @author Ahmed
 */
public class FunkyNumbers {

    public static boolean isTriangularNumber(long num) {
        if(num == 0)
            return false;
        long t = (long) Math.sqrt(2*num);
        return t * (t+1) == 2*num;
    }

    public static void main(String[] args) {
        Scanner scan = new Scanner(System.in);
        int n = scan.nextInt();
        String res = "NO";
        
        int m = (int) Math.sqrt(n);
        for (int i = m; i > 0; i--) {
            if (isTriangularNumber(n - (i * (i + 1) / 2))) {
                res = "YES";
                break;
            }
        }
        
        System.out.println(res);
    }
}